An integral inequality for the invariant measure of a stochastic reaction-diffusion equation

作者：Da Prato Giuseppe^*; Debussche Arnaud

来源：Journal of Evolution Equations, 2017, 17(1): 197-214.

DOI：10.1007/s00028-016-0349-z

• Reaction-diffusion equations
• invariant measures
• Fomin differentiability
• surface integrals in Hilbert spaces

We consider a reaction-diffusion equation perturbed by noise (not necessarily white). We prove an integral inequality for the invariant measure nu of a stochastic reaction-diffusion equation. Then, we discuss some consequences as an integration by parts formula which extends to nu a basic identity of the Malliavin Calculus. Finally, we prove the existence of a surface measure for a ball and a half-space of H.

• 出版日期2017-3